On the first 5 tests of his history class, Omar got an average score of 80. What does he need on the next test to have an overall average of 83?
Answer: Let his score on the next test be $x$ The sum of all of his scores is then $5 \cdot 80 + x$ The same sum must also be equal to $6 \cdot 83$ Solve: $x = 6 \cdot 83 - 5 \cdot 80 = 98$.